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二层随机规划逼近问题最优解集的上半收敛性

霍永亮   

  1. 重庆文理学院数学与财经学院数学研究所,  重庆 402160
  • 收稿日期:2013-06-14 出版日期:2014-06-25 发布日期:2014-10-13

霍永亮. 二层随机规划逼近问题最优解集的上半收敛性[J]. 系统科学与数学, 2014, 34(6): 674-681.

HUO Yongliang. THE UPPER SEMI-CONVERGENCE OF OPTIMAL SOLUTION SETS OF APPROXIMATION PROBLEMS FOR BILEVEL STOCHASTIC PROGRAMMING[J]. Journal of Systems Science and Mathematical Sciences, 2014, 34(6): 674-681.

THE UPPER SEMI-CONVERGENCE OF OPTIMAL SOLUTION SETS OF APPROXIMATION PROBLEMS FOR BILEVEL STOCHASTIC PROGRAMMING

HUO Yongliang   

  1. College of Mathematics and Finance, Institute of Mathematics, Chongqing University of Arts and Sciences, Chongqing 402160
  • Received:2013-06-14 Online:2014-06-25 Published:2014-10-13
在下层初始随机规划问题可行解集上引入了正则的概念,并在下层初始随机规划最优解唯一的条件下, 利用上图收敛理论,给出了下层随机规划逼近问题的任意一个最优解向量函数都连续收敛到下层初始随机规划问题的唯一最优解向量函数.然后将下层随机规划的最优解向量函数反馈到上层随机规划的目标函数和约束条件中,
得到了上层随机规划逼近问题的最优解集关于最小信息概率度量收敛的上半收敛性.
In this paper, we define the concept of regularity of feasible set for lower level original  stochastic programming. If  optimal solution set for lower level original  stochastic  programming is a set of single points, by using the epi-convergence theory,  we  show  that any optimal solution  vector function for lower level  stochastic programming approximation problem   converges continuously to the unique optimal solution vector function for  lower level original  stochastic programming. Furthermore, if objective  function and constraint conditions of  upper level  stochastic programming contain optimal solution vector function of lower level stochastic   programming, if probability measure sequence is convergence,  we obtain the upper semi-convergence of  optimal solution set for upper level  stochastic programming in minimal    information probability metric.

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[1] 霍永亮;刘三阳. 非线性参数规划问题$\varepsilon$-最优解集集值映射的连续性[J]. 系统科学与数学, 2009, 29(6): 735-741.
[2] 霍永亮;刘三阳. 概率约束规划逼近最优解集的稳定性和最优值的连续性[J]. 系统科学与数学, 2007, 27(6): 908-914.
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